On the 'auction site' which shall remain anonymous there are a number of LED strobe lights which you could use and they are not expensive. Instead of the reflector rotating they just light up in sequence as if going round.

As Ian says, it is the shield /reflector that controls the light beam. The amount of arc of a circle that the shield covers and the speed of rotation will determine the frequency/duration of the light. I suspect that the shape of the reflector may determine the width or concentration of the light beam. I imagine that for model purposes it doesn't need to be too intense.
edit: If you're ever down this way the older of the two lighthouses at Dungeness is usually open to the public (if you have a head for heights) . An added bonus is the adjacent RH&DR station.
You may have redundant lighthouses open to the public in Suffolk I guess.

As Ian says, it is the shield /reflector that controls the light beam. The amount of arc of a circle that the shield covers and the speed of rotation will determine the frequency/duration of the light. I suspect that the shape of the reflector may determine the width or concentration of the light beam. I imagine that for model purposes it doesn't need to be too intense.

The light is also controlled by a special type of lens, but I agree for model purposes I think that's going too far.

My other thought is there were some on that auction site. It might be possible to use the equipment in your own build.

Personally, I wouldn't recommend trying to modify the solar powered garden lighthouses. My wife is a sucker for anything like that and we have had two of them. They are great when new but only last a couple of months before they pack up and stop rotating, then the LED goes subsequently. I did manage to breathe temporary new life into one of them but it went again after a very short length of time.
The other point is of course that they are very small even for 16mm and for 7/8" they would look ridiculous.